Re: References for Numerical Integration

[bradklee@gmail.com]

Hi Kevin,

You’re working with differentiably finite (or holonomic) functions, 

so it should be fast and easy to calculate definite integrals from 

partial sums of series representations. However, with oscillating

functions you usually need a piecewise decomposition between

roots. I am busy now, but may try to write an example calculation

later next week.

In the industry of polynomial integrals, the “chebfun” project is a 

very well known competitor [1]. Maybe you could try to implement 

something similar in Pari?

Cheers,  Brad

[1] http://www.chebfun.org/docs/guide/

On Oct 21, 2018, at 5:00 PM, kevin lucas <lucaskevin296@gmail.com> wrote:

Thanks, I'll check it out. Any other references would also be appreciated.

Kevin

On Sun, Oct 21, 2018 at 10:40 PM Dirk Laurie <dirk.laurie@gmail.com> wrote:

<ad>
Have a look at Chapters 1 and 9 of the book "The SIAM 100-digit
Challenge: a Study in High-Accuracy Numerical Computing".
</ad>

Pari-GP 2.2.8 code (inter alia) is on the site:
http://www-m3.ma.tum.de/m3old/bornemann/challengebook

-- Dirk
Op So., 21 Okt. 2018 om 19:35 het kevin lucas <lucaskevin296@gmail.com> geskryf:
>
> PARI obviously has some very powerful tools for numerical integration. I have, however, keenly felt the absence of a text treating this area in more detail than the manual. I was recently trying to compute
> intnum(x=0,oo, (sin(x)^4)/(x)^2)
> I only get about 3 digits (the integral evaluates to log(2)). There's probably a neat way to get more digits in this particular instance. What I'm looking for is a reasonably complete account of such methods, for even more complicated integrals in PARI. I have, for instance met the integral
> intnum(x=0,oo, exp(x)*besselj(0,x))
> which doesn't even return an answer. Where can I learn how to evaluate such integrals in GP?
>
> References outside just numerical integration are also welcome.
>
> Thanks,
> Kevin